Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple extension of this problem with three indentical masses and four identical springs. Solve for the physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two masses. We also refered to these values and vectors together as the eigen modes. I expect that we will have short discussions about the solution for the motion in each class period. Me Ya > differences displacement k K 7mm Jum M q Lakan M M 7mm A X
Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple extension of this problem with three indentical masses and four identical springs. Solve for the physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two masses. We also refered to these values and vectors together as the eigen modes. I expect that we will have short discussions about the solution for the motion in each class period. Me Ya > differences displacement k K 7mm Jum M q Lakan M M 7mm A X
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
can u check my 1st part calculations
![Md ² tb
+K (Y₂ - Ya) -K (^YC - 1₂) = 0
K[ (a + (Yo - Ya) - (^Y₁ - 7b) -
-90
= 1 [X + (46-4₂) _d₂] = K[X + ("Pc - 4₂ ) - 0₂] = 0
KL-Ya +(24/b - c)]
41
+K²c + K (Yc-7₂) = 0
d+²
M
O
Ya
21
O
O
O
M
O
Y
2k -k
M
o
For natural frequencies
Vj = Aje i at
Yj =-Ajw² eint
2к- маг
O
-k
We use Mw² = a
=
zfp
kata
PN ₂P W
2K-Ma²
-K
オー
+
2k
we take
Q =
O
2K-MW²
Ye
A
с
O
O
=
O
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50130201-d9ba-49f8-bcaa-a82c73687787%2F6664a05a-e732-49ab-81ea-2fd4223d7718%2Ft02jdw9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Md ² tb
+K (Y₂ - Ya) -K (^YC - 1₂) = 0
K[ (a + (Yo - Ya) - (^Y₁ - 7b) -
-90
= 1 [X + (46-4₂) _d₂] = K[X + ("Pc - 4₂ ) - 0₂] = 0
KL-Ya +(24/b - c)]
41
+K²c + K (Yc-7₂) = 0
d+²
M
O
Ya
21
O
O
O
M
O
Y
2k -k
M
o
For natural frequencies
Vj = Aje i at
Yj =-Ajw² eint
2к- маг
O
-k
We use Mw² = a
=
zfp
kata
PN ₂P W
2K-Ma²
-K
オー
+
2k
we take
Q =
O
2K-MW²
Ye
A
с
O
O
=
O
O
![Chapter 1 of "Waves", by F.S. Crawford, Jr.
Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple
extension of this problem with three indentical masses and four identical springs. Solve for the
physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two
masses. We also refered to these values and vectors together as the eigen modes. I expect that we
will have short discussions about the solution for the motion in each class period.
1
1
7₁
Ye
displacement!
difference
K
k
Immu
1
M
M
force balance
on the masses
Assuming Ye > 146 > to initially
b
ма гана
+k Ya- (Nb-7a) k = 0
d+²
k (a + (xb-7a) - 9₂) = 0
(Y6-Ya)
- k (p² + (Pb - Ya) ~) - K (x + 7 -/00) = 0
K [= (₂-4a) - Ya)] =
= K Ya ₁= (b - Ya) k = 0
1
wm
M
-a-
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50130201-d9ba-49f8-bcaa-a82c73687787%2F6664a05a-e732-49ab-81ea-2fd4223d7718%2F9uv6w13k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Chapter 1 of "Waves", by F.S. Crawford, Jr.
Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple
extension of this problem with three indentical masses and four identical springs. Solve for the
physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two
masses. We also refered to these values and vectors together as the eigen modes. I expect that we
will have short discussions about the solution for the motion in each class period.
1
1
7₁
Ye
displacement!
difference
K
k
Immu
1
M
M
force balance
on the masses
Assuming Ye > 146 > to initially
b
ма гана
+k Ya- (Nb-7a) k = 0
d+²
k (a + (xb-7a) - 9₂) = 0
(Y6-Ya)
- k (p² + (Pb - Ya) ~) - K (x + 7 -/00) = 0
K [= (₂-4a) - Ya)] =
= K Ya ₁= (b - Ya) k = 0
1
wm
M
-a-
-
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